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%I #7 Feb 21 2024 01:19:27
%S 1,120,4020,121220,1651220,23551220,266251220,2750051220,25551151220,
%T 210564451220
%N Powers of ten in factorial base.
%C Next term has a "ten" digit.
%C Also called factoradix.
%C With hexadecimal extended to use the whole alphabet, the sequence continues: 17a5726651220, 12092315551220, b6781182251220, 799b90920051220, 4c71069221151220, 2dcaa584234451220, 1a1f264b9386651220, fb2797aa5975551220, 8437c58494852251220, 423g9bad8a4580051220, 1k213c54aa81881151220
%C 10^48 needs a "36" digit. We can say with high probability that 10^64 is the last value that can be written without needing any digits larger than 35 (checked up to 10^1400, where it is vanishingly unlikely).
%H Jonathan Wellons, <a href="http://snollew.blogspot.com/2008/06/factorial-base.html">The Factorial Base</a>, 2008.
%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>.
%F a(n) = A007623(A011557(n)). - _Amiram Eldar_, Feb 21 2024
%e 10000 = 1 * 7! + 6 * 6! + 5 * 5! + 1 * 4! + 2 * 3! + 2 * 2! + 0 * 1!. Hence 10000 is 1651220 in factoradix.
%t a[n_] := Module[{k = 10^n, m = 2, r, s = {}}, While[{k, r} = QuotientRemainder[k, m]; k != 0|| r != 0, AppendTo[s, r]; m++]; FromDigits[Reverse @ s]]; Array[a, 10, 0] (* _Amiram Eldar_, Feb 21 2024 *)
%Y Cf. A007623, A011557.
%K base,easy,nonn
%O 0,2
%A Jonathan Wellons (wellons(AT)gmail.com), Jun 08 2008